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Different forms of 











ased in Elbows. 



ELBOW PATTERNS 



FOR 



ALL FORMS OF PIPE 



A TREATISE UPON THE ELBOW 
PATTERN EXPLAINING THE MOST 
SIMPLE AND ACCURATE METHODS 
FOR OBTAINING THE PATTERNS 
FOR ELBOWS IN ALL FORMS OF 
PIPE MADE FROM SHEET METAL 

WITH USEFUL MATHEMATICAL RULES 
AND TABLES 

' SECOND EDITION, ENLARGED 



BY 

F. S. KIDDER 






PUBLISHED BY 

THE SHEET METAL PUBLICATION CO. 

Tribune Building, New York 

1918 






' 



Copyrighted, 1912, 1918 

BY 

THE SHEET METAL PUBLICATION CO. 



OCT 14 1918 



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iTRAPES|j'K£| 1 |cOUHCIL» 



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PREFACE 

The importance of a quick and accurate 
method of securing patterns for elbows, has in- 
duced the writer to lay before the Sheet Metal 
Worker in the following pages, methods which 
may be employed in securing the patterns for 
elbows of any angle or number of pieces in all 
forms of pipe. Methods are here pointed out 
which admit of the least display, and the greatest 
accuracy, without that study of geometrical work 
usually recommended. 

In other words, if we possess a pair of com- 
passes and straightedge, we can produce patterns 
for elbows in round pipe of any size, angle, or 
number of pieces. With very little additional 
attention, we are enabled to produce the patterns 
for elbows of all forms of pipe with the greatest 
accuracy and in the least possible time, which 
is an important factor in these days of sharp 
competition. 

F. S. K. 
iii 



CONTENTS 

PART I 

PAGES 

An Analysis of the Forms Involved in Producing 
the Patterns for Elbows in Round Pipe.. i-8 

PART II 
Patterns for Elbows in Round Pipe 9-23 

PART III 
Patterns for Elbows in Pipe of any form 24-53 

PART IV 

Patterns for Riveted Elbows to be made from 

Heavy Iron 54~7 2 

Appendix 73-88 

Index 89-91 

iv 



ELBOW PATTERNS 

PART I 

AN ANALYSIS OF THE FORMS INVOLVED IN 
PRODUCING THE PATTERNS FOR ELBOWS IN 
ROUND PIPE 

Fig. i illustrates a four pieced 90 degree 
elbow, .and upon reducing this to its simplest 
form, we find it contains three elbows at an angle 
of 30 degrees. When it is stated that it contains 
three elbows at an angle of 30 degrees, it should 
be remembered that the term 30 degrees is to 
an extent shop phraseology, since angles are 
measured by the position the two lines of which 
they are formed occupy as radii of a circle. 
This places what is usually termed 30 degrees 
at 150 degrees, unless the axis of one arm of 
said angle or elbow is presumed to be parallel 
to a right line in space, then will the axis of 
the second arm be at an angle of 30 degrees to 
said right line. The writer has in this work, 



ELBOW PATTERNS 



used the usual shop term, or the number of 
degrees the elbow varies from a right line. 
While the illustration Fig. i, shows only an 



Fig. i. — Illustrating a four-pieced square elbow, which when 
reduced to its simplest form contains three elbows at an 
angle of 30 degrees. 

elbow of four pieces at an assumed angle of 
90 degrees, the reader can readily conceive how 
the above principles may be adapted to elbows 
of any angle or number of pieces. In every case, 



ANALYSIS 6 

the required number of component elbows is 
dependent upon the required number of pieces, 
the angle of which is also dependent upon the 
required angle of the finished elbow. For 
example, let it be presumed that an elbow is 
required to be made in three pieces at an angle 
of J2 degrees, we then have two component 
elbows at an angle of 36 degrees : and had the 
specification called for this elbow in five pieces, 
then four component elbows at an angle of 18 
degrees would have been required. 

Thus in every instance, we may deduct one 
from the number of pieces required in the 
finished elbow, then will the remainder represent 
the number of component elbows required: and 
by dividing the specified angle in degrees of the 
finished elbow, by the number representing the 
component elbows, we find the required angle of 
each component. As an example, let it be 
presumed that an elbow is required to be made 
in six pieces at an angle of 80 degrees, the 
mathematical solution would appear thus — 
8o°-=-(6— i) = i6°. 

A graphical solution may be arrived at by the 
use of our compasses and straightedge as shown 
at Fig. 2, by drawing an indefinite right line as 



4 ELBOW PATTERNS 

a b, and from any point on this line as center as 
at c, describe an arc of convenient radius. 

Presuming the bevel to have been set to the 
required angle of the finished elbow, (in this 
instance 80 degrees) place it in position as shown, 
i.e., one arm parallel to line a b, with vertex of 




Fig. 2. — Showing a graphical method of obtaining the angle 
of the component elbow. 



angle at point c, when point d may be located. 
Upon dividing the arc b d, into one less number 
of equal parts than pieces required in the finished 
elbow, the point e is established in the first 
division from b : and by drawing a line from 
point c, intersecting point e, the required angle 
of the component elbow is shown at a c e, i.e., 
16 degrees. 



ANALYSIS O 

From what has been shown, it is evident that 
the use of the protractor will greatly facilitate 
the work, but it is by no means necessary. It 
is also evident that when called upon to produce 
the patterns for an elbow of any angle, or number 
of pieces beyond two, we have only to secure 
the curved line upon which one piece of the 
component elbow is cut, and duplicate for the 
whole. Therefore the important factor to be 
determined is, at what angle to the base of a 
right cylinder must a plane be presumed to cut 
its curved surface to produce a line, whose 
development upon a flat surface will constitute 
the curved line of the required pattern : presum- 
ing the diameter of said cylinder is equal to the 
diameter of pipe for which the elbow is to be 
made. 

The above statement is exemplified in the so- 
called adjustable elbow, inasmuch as its sections 
may be so revolved as to form either a piece of 
straight pipe, or an elbow, whose angle is 
dependent upon the number of sections, together 
with the angle each section is cut to its axis. 

Fig. 3 illustrates an adjustable square elbow, 
made in four pieces which have been so revolved 
as to form a piece of straight pipe, and as each 



ELBOW PATTERNS 



section is cut at the same angle to its axis, when 
we determine the angle of one, we know the 
angle of all. 




Fig. 3. — Illustrating an adjustable square elbow with sections 
so revolved as to form a piece of straight pipe. 



If we presume to remove two sections and 
revolve them so that their shortest portions 



ANALYSIS 



intersect, we form a simple elbow made of two 
pieces, at an angle of 30 degrees, which is one 
of the three components of the whole elbow, and 
to produce the patterns for this, we must 




Fig. 4. — Showing elevation of simple or component 

elbow. 



determine how much longer should each piece 
be at the heel than at the throat. This can be 
determined by bisecting the angle : as for 
example, the angle is said to be 30 degrees, and 
upon bisecting same, we obtain 15 degrees as the 



8 ELBOW PATTERNS 

inclination of section line to bases of cylinders 
when placed in elevation as shown at Fig. 4. 

Portions of said elevation are right angled 
triangles as shown at a b c, and a d c : the bases 
of which are equal in length to the diameter of 
pipe for which the elbow is to be made, with 
perpendiculars equal to the altitude of the re- 
quired heels. We may construct such a triangle 
independently, since it is possible to obtain the 
length of the perpendicular, when the magnitude 
of two angles and the length of base are known, 
thereby avoiding the necessity of producing a 
complete elevation. 



PART II 

PATTERNS FOR ELBOWS IN ROUND PIPE 

From what has been demonstrated in Part I. 
we may deduct the following Rules to obtain 
the altitude of heel for elbows of any size, angle, 
or number of pieces. 

Rule i. — Divide the required angle of the 
finished elbow by a number which is one less than 
the number of pieces required, then will the 
quotient be the required angle of the component 
elbow. 

Rule 2. — Divide the required angle of a 
simple, or component elbow by two, then will 
the quotient represent the angle of the hypoth- 
enuse to the base of a right angled triangle, 
whose perpendicular will furnish the altitude of 
heel, providing its base is equal in length to 
diameter of pipe for which the elbow is to be 
made. 

To illustrate the application of the above 
Rules, let it be presumed that the patterns are 

9 



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ELBOW PATTERNS 




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IN ROUND PIPE 11 

required for an elbow to be made in four pieces, 
for a 12 inch pipe, of a given angle to which the 
bevel has been set. 

In using the protractor, we may place the 
bevel in a position as shown at Fig. 5, when we 
find the angle to read 84 degrees : then by Rule 1, 
the angle of the component elbow is found to 
be 28 degrees, after which we apply Rule 2, and 
find the inclination of section line to be 14 
degrees. 

If we use the graphical method, we may look 
upon the arc m n Fig. 5, as the arc of con- 
venient radius, (spoken of in connection with 
Fig. 2, Part I) which has been described from 
point p as center. With bevel in position as 
shown, point »y is located, w r hen we apply Rule 1 
to the use of our compasses in dividing are s 0, 
thereby locating point t. Rule 2 may be applied 
to arc t to locate point u, and upon drawing 
line p u, it will be noted that we secure identical 
results, i.e., we note that line p u makes an angle 
of 14 degrees to line p 0. 

Upon making base line p zv equal in length 
to diameter of pipe for which the elbow is to be 
made, (12 inch) and erecting a perpendicular as 
w v Fig. 5, by measuring same, we find the 



12 



ELBOW PATTERNS 



necessary altitude of heel to be 3 inches for the 
required elbow, i.e., an elbow for 12 inch pipe, to 
be made in four pieces, at an angle of 84 
degrees. 

As has been shown, Fig. 5, the required 
inclination of section line has been found to be 
at an angle of 14 degrees to the base line p o, 




Fig. 6. — Illustrating method of obtaining the altitude of heel 
by the use of the steel square. 

and with the bevel set to that angle, we may, if 
we choose employ the steel square to determine 
the altitude of heel, as shown Fig. 6, which needs 
little explanation to enable the reader to note 
that we secure the same result, i.e., an altitude 
of 3 inches. 

By placing one arm of the bevel in contact 
with the blade, and with vertex of angle at the 
mark indicating the diameter of pipe for which 



IN ROUND PIPE 13 

the elbow is to be made: the second arm of 
bevel will be found to intersect the 3 inch mark 
upon the tongue of the square as shown. 

To produce the curved line upon which the 
pattern is cut, we may employ either of two 
methods hereinafter shown, and designated as 
First, and Second. The First method is one 
which may be followed with the least number 
of tools, and satisfactory results secured in the 
shortest possible time. 

First method of producing the curved line upon 
which an elbow pattern is cut 

Upon turning attention to Fig. 7, the reader 
will note the representation of a piece of sheet 
metal at A, B, C, D, from which it may be 
assumed an elbow is to be made: i.e., it may be 
assumed that the elbow is for a pipe of a given 
size, and that this piece of sheet metal is of 
correct length, with seams added. 

At any required distance from edge C D, a line 
may be drawn as E E. With compasses set to 
a distance equal to one-half the required altitude 
of heel, (found as previously explained) place 
one point at points E. and locate points F, with 
points F as centers, and F E as radius, describe 




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IN ROUND PIPE 



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the semi-circles as shown, thus locating points G 
when lines F F, and G G may be drawn. With- 
out changing adjustment of compasses, and 
using points E as centers, describe the small 
arcs as at 3. With points G as centers, describe 
arcs as at 5, and with points 4 as centers, describe 
arcs as shown at 2 and 6, thus dividing each 
semi-circle into six equal parts, when lines are 
drawn as 2 2, 3 3, etc. Bisect C D as at H, and 
draw the perpendicular H k. With compasses 
so adjusted as to divide the line G k into six 
equal parts, place one point at a, and mark points 
b b. From point c, step two spaces each way, 
marking the points d d : from point e, step three 
spaces each way, and mark points / /. To 
shorten the work we may now step two spaces 
from points g, thus locating points h h, and one 
space from points i locates points / j, thus 
securing points k b d f h j i, through which the 
curved line may be traced. 

Upon cutting this piece, i.e., C E k E D, a 
pattern is secured which may be duplicated for 
the required number of pieces as shown. 

The accuracy of the foregoing method may 
perhaps be questioned for the reason that the 
circumference of the pipe is divided into so few 



16 ELBOW PATTERNS 

parts. It may be stated that such criticism is 
justified from a scientific standpoint : however 
this may be overcome in a practical way when 
cutting the pattern, if it is remembered that the 
points secured are in correct positions, but the 
straight lines usually drawn between those points 
are not correct, inasmuch as they should be more 
or less curved. Therefore if the shears are 
swung between points so as to cut a curved 
instead of a straight line, a very little practice 
will overcome this objection to a great extent. 
However the second method may be employed to 
secure any degree of accuracy. 

Second method of producing the curved line 
upon which an elbow pattern is cut 

The inclination of section line as shown at 
i a, Fig. 8, may be determined by any method 
previously explained. In Fig. 8, a graphical 
solution has been arrived at by employing the 
arc of convenient radius in the following manner. 

Draw an indefinite right line as A B, and 
from any point as center as at i, draw an arc 
of convenient radius as shown at b c f. Set the 
bevel to the required angle of the finished elbow 



IN ROUND PIPE 



17 



(84 degrees in this instance) and place it in 
position as shown at Fig. 2, Part I, thus locating 
point c. By Rule 1, (presuming the elbow is to 
be made in four pieces) point d is located. By 




Fig. 8. — Showing the plan and elevation of a sufficient 
portion of the elbow to supply all measurements required 
to complete the pattern. 



Rule 2, locate point c, through which the line 
1 a is drawn, thereby determining the inclination 
of that line to A B. 

With the compasses set to a distance equal 
to one-half of the diameter of the pipe for which 





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the elbow is to be made, place one point at i and 
locate point g. Without altering adjustment of 
compasses, with point g as center draw the 
semi-circle 159. Divide the semi-circle 159 into 
any desired number of equal parts as at 1 2 3 4 
etc., and draw right lines from said points of divi- 
sion perpendicular to line A B to intersect line 1 
a as shown. Thus the plan and elevation of a 
sufficient portion of the elbow has been drawn, 
together with a number of right lines presumed 
to be upon its surface, furnishing all necessary 
measurements required to complete the pattern, 
i.e., for an elbow to be made in four pieces, at 
an angle of 84 degrees. 

Select a piece of material whose length is equal 
to the circumference of the pipe for which the 
elbow is to be made, or double the length of semi- 
circle 159, Fig. 8, as shown at C D E F, Fig. 9, 
with seams added. At a suitable distance from 
the edge E F, draw a line as 1 1 and bisect it as 
at point 9. From point 9, draw a perpendicular 
line as shown by 9 h prolonged. Divide lines 1 9 
into the same number of equal parts as the semi- 
circle 159, Fig. 8, has been divided into, and 
from these points of division, draw perpendicular 
lines as shown at 2 3 4 5, etc. By the use of the 




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IN ROUND PIPE 21 

compasses, transfer lengths of lines found be- 
tween lines i B and i a, Fig. 8, to lines of similar 
numbers from i I, Fig. 9, thus locating points 
through which the curved line of the pattern is 
traced as shown. 

When the piece 1 h 1 E F is cut, it may be 
revolved or reversed and used as a pattern for 
tracing the remaining curved lines as shown. 

Fig. 10 illustrates the different assignment of 
numbers to the lines when the seams are required 
upon the side, instead of at the throat and heel, 
which is the only difference in producing such 
patterns. Numbers can be so arranged as to 
locate the seam upon any one of the lines, which 
are in reality, elements of the cylindrical surface 
of which the elbow is composed. 

In many branches of sheet metal work, the 
length of each piece in the throat is a matter of 
convenience, there being no special importance 
attached to it, further than to make it 
sufficiently long to be handled in the making 
up : or perhaps short enough to economize in the 
matter of material. However in some branches, 
a specified radius of throat is demanded, in 
which case the elbow is often made in a con- 
siderable number of pieces. 



22 



ELBOW PATTERNS 



To secure the length of each piece in the throat 
for an elbow of any required radius 

Draw an indefinite right line as a b, Fig. n, 
and from any convenient point upon this line as 




Fig. ii. — Illustrating a graphical method of determining the 
length of each piece in the throat, for an elbow of any 
required radius. 

center, describe an arc whose radius is equal to 
the radius of the required elbow, as c d b. 
Locate by Rules i and 2 a line which will be at 
the proper angle to line a & to represent the 
section line for an elbow of the same angle and 
number of pieces, as shown by line e d Fig. 11, 



IN ROUND PIPE 



23 



where it has been presumed that an elbow was 
required to be made in seven pieces, at an angle 
of 90 degrees, thus locating line d c at an angle 
of yy 2 degrees to line a b. From point b, draw 
a line perpendicular to line a b, which intersects 
line d e at the point /, then will the length of 
line b f equal one-half the length of each piece in 
the throat for an elbow of the required radius 
and number of pieces, regardless of size. The 
necessary allowance for seams must be added to 
the above measurements. 

In making elbows, it is sometimes found 
there is a variation in the angle, i.e., the finished 
product will not answer true to name. The 
cause for this is usually found in the fact that 
the edges have not been turned the same width 
at the throat as at the heel, a variation often 
found when machines of the older type are 
used. Patterns are usually developed on the 
presumption that the seam will be the same 
width throughout, and if found this is not 
accomplished, the section line may be so adjusted 
as to overcome it. In elbows of two pieces the 
difference will be slight, but as the number of 
pieces is increased, this variation increases to a 
point where it must be remedied. 



PART III 
PATTERNS FOR ELBOWS IN PIPE OF ANY FORM 

Methods of securing the patterns for elbows 
in forms of pipe other than round, differ in no 
essential respect, since in every instance the 
same inclination of section line will prevail for 
elbows of the same angle, or number of pieces, 
regardless of the form of pipe for which it is to 
be made. The difference is simply in that portion 
of the diagram which represents the form of 
pipe. This must, in every instance, be a true 
representation of the form of pipe for which the 
elbow is required, or what is usually termed, 
a cross-section of it, unless said form consists 
of two equal and opposite parts, in which case, 
either part will fulfill every requirement, since 
it may be duplicated for the other. 

In forms whose diameters are not constant, it 
becomes somewhat difficult to designate which 
way the elbow is to turn : as for example, it may 
be required to make a square elbow in oblong 

24 




Fig. 13, r 

Figs. 12 and 13.— Showing a method of designating which 



way an elbow is to turn. 



25 



26 ELBOW PATTERNS 

pipe, when the question arises, Which way is 
the elbow to turn ? This is perhaps best answered 
by the use of simple diagrams as shown at Figs. 
12 and 13. 

Figs. 12 and 13 may be looked upon as the 
representations of elbows, and the oblong 
diagram at A as the form of pipe. The same 
methods are employed for each, although the 
finished patterns show some variation in appear- 
ance: therefore diagrams are herein shown to 
illustrate the development of each. 

To secure the patterns for an elboiv in oblong 
pipe, turning parallel to the plane of the 
major axis of said pipe, as shown at Fig. 12 

The diagrams are drawn in the same general 
manner as previously explained, and shown at 
Fig. 14, where the graphical method has been 
employed to determine the inclination of section- 
line, presuming the elbow is to be made in three 
pieces, and at an angle of 90 degrees. For 
example, the indefinite right line 1 9 is drawn, 
and from any point upon this line as center as 
at 1, describe the arc of convenient radius as 
b d /. 



IN ANY FORM OF PIPE 



27 



Upon applying the bevel as shown at Fig. 5, 
Part I, point c is located. By Rule 1 we find 
point d, and by Rule 2 locate point e through 
which the section-line 1 a is drawn. As shown 



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secured. 



at Fig. 12, the pipe is required to turn parallel 
to the plane of its major axis, therefore in Fig. 
14 its representation, or a necessary portion of 
it is placed with its longest diameter parallel to 
the base of triangle 1 a 9. Divide the curved 
portions of the diagram which represent the 



28 ELBOW PATTERNS 

form of pipe, into a number of equal parts as at 
1234, etc. 

Draw lines from said points of division, 
perpendicular to the base of triangle, intersecting 
its hypothenuse as shown, thus establishing 
lengths of lines to be transferred to the material 
upon which the pattern is to be developed. Upon 
this piece of material, which is understood to 
be equal in length to the circumference of pipe, 
draw a line as 1 1, Fig. 15 at any required 
distance from one edge. 

Locate points upon this line at the same 
relative distance from each other as found upon 
the diagram representing the form of pipe in 
Fig. 14, remembering that this diagram repre- 
sents one-half the pipe only, and must be 
duplicated to complete the whole circumference, 
and that there must be allowance made for seams, 
as shown, Fig. 15. 

From said points draw indefinite right lines 
perpendicular to 1 I. Transfer distances as 
found upon triangle 1 a 9, in lines 1234, etc., 
Fig. 14, between their intersection with line 1 a 
and 1 9, to lines of similar numbers upon the 
material from which it is proposed to cut the 
pattern, setting off said distances from line 1 1, 







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30 ELBOW PATTERNS 

thus locating points through which the curved 
line is traced. Cut the material upon this line, 
thereby securing a piece which is used for a 
pattern in tracing the additional curved line as 
shown, to complete the patterns for an elbow 
as above specified. 

To secure the patterns for an elbow in oblong 
pipe, when it is required to turn said pipe 
parallel to the plane of its minor axis as 
illustrated at Fig. 13 

By comparing Figs. 14 and 16, the reader will 
note that the only variation in determining the 
lengths of lines, is in the position of that portion 
of the diagram which represents the form of 
pipe. In Fig. 16, it has been so revolved as to 
place its short diameter parallel to the base line 
of triangle. 

The inclination of the hypothenuse of said 
triangle to the base line a b is established when 
the necessary inclination of section line is 
determined, in precisely the same manner as 
previously explained, which in this example is 
22y 2 degrees, since it is assumed that the 
patterns are required for an elbow to be made 
in three pieces, at an angle of 90 degrees. 



IN ANY FORM OF PIPE 



31 



Upon placing the diagram which represents 
the form of pipe, or a suitable portion of it, in 
a position as shown at Fig. 16, divide the curved 















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secured. 

portion into a number of equal parts. From 
said points of division, draw lines perpendicular 
to line a b interacting lin<? a c, then will that 
portion of those lines contained within the 
triangle lepresent lengths to be transferred to the 
sheet upon which the pattern is to be developed. 



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CC 


M 

+-> 
+-> 

ft 




o 

CO 
1 








CQ 


1. 


I 


/ 




\ 


/ 


CO 


o 


\ 


/ 


s 


\ / 


*tf 




\ / 


id 




\ I 







IN ANY FORM OF PIPE 33 

Upon the piece of material from which the 
elbow is to be made, whose length is equal to 
the circumference of the pipe, with the necessary 
allowance for seams added, draw a line at any 
desired distance from one edge, as shown by 
line 5 5, Fig. 17. 

Locate points upon line 5 5, at the same 
relative distance from each other as found on 
that portion of the diagram representing the 
form of pipe in Fig. 16, remembering that, as 
shown in Fig. 16, it represents only one-half the 
circumference of the pipe, which must be 
duplicated for the other half. Points located 
upon line 5 5, Fig. 17, have in this instance been 
so numbered as to place the seam at the side, 
which is perhaps the best position for an elbow 
of this class. From said points draw indefinite 
right lines, perpendicular to line 5 5. Transfer 
distances as found upon triangle a d b, in lines 
1234, etc., to lines of the same number upon 
the material, thus locating points through which 
the curved line of the pattern is traced. Cut the 
material upon this line, and reverse or revolve 
the piece to trace the additional line, as shown 
at Fig. 17. 



34 ELBOW PATTERNS 

To secure the patterns for an elbow in elliptical 
pipe j when it is required to turn said pipe 
parallel to the plane of its major axis 

In the development of patterns for elbows in 
elliptical pipe, the reader should experience 
little difficulty, providing he has secured an 
understanding of what has been previously 
discussed. The main difficulty is perhaps in one's 
inability to describe a proper form of section. 

The writer has made it a practice, when called 
upon to produce the patterns for elbows in 
elliptical pipe, to make a templet, with its major 
and minor axis marked upon it.* By the aid of 
this templet the production of elbow patterns 
for elliptical pipe becomes as simple as any 
previously discussed. 

In Fig. 1 8, the necessary inclination of section 
line has been determined by the graphical method 
as follows: Draw the indefinite right line a n, 
and from point I as center with any convenient 
radius, describe an arc as b c d /. . Place the 
bevel in position as shown at Fig. 5, Part I, thus 
locating point c. By Rule 1, point d is located, 

* Methods of describing the ellipse will be found in 
the Appendix. 



IN ANY FORM OF PIPE 



35 



and by Rule 2, locate point e, through which the 
line 1 e g is drawn, thereby establishing the in- 
clination of section line when the elbow is to be 
made in six pieces, and at an angle of 90 degrees. 




Fig. 18. — Showing diagram from which lengths of lines are 

secured. - 



(Variation of angle, or the number of pieces, 
have been fully discussed in the foregoing 
pages.) Place the semi-form of pipe in position 
as shown by line 1 6 11, Fig. 18, and divide this 
curved line into a number of equal parts as shown 



IN ANY FORM OF PIPE 37 

at points 1234, etc. From said points of 
division draw right lines perpendicular to line 
a 11, to intersect line 1 g, then will those lines 
between lines ill, and 1 g, furnish the necessary 
lengths to be transferred. 

Upon a piece of material whose length is equal 
to the circumference of pipe, (with seams added) 
for which the elbow is to be made, draw a line 
as 1 1, Fig. 19 at any required distance from 
one edge. 

Locate points upon line 1 1, at the same 
relative distance from each other as shown in 
points 1234, etc., Fig. 18. 

Erect perpendiculars as shown, upon which 
set off distances from line 1 1, as found in lines 
shown between lines in, and 1 g, Fig. 18 upon 
lines of a similar number in Fig. 19, thus locating 
points through which the curved line is traced, 
and duplicated to complete the pattern, as shown. 

To secure the patterns for an elbow in elliptical 
pipe, when it is required to turn said pipe 
parallel to the plane of its minor , axis 

In the development of patterns for elbows as 
above described, the reader will note, upon turn- 
ing attention to Figs. 20 and 21, that the only 



38 



ELBOW PATTERNS 



variation from the one last discussed, is in the 
position the semi-form of pipe occupies as 
regards the base of triangle from which the true 



lengths of lines are secured. 




Fig. 20. — Showing diagram from which lengths of lines are 

secured. 



Figs. 20 and 21 show the necessary diagrams 
to secure the patterns when it is required to 
turn the pipe parallel to the plane of its minor 
axis, and as will be noted, the minor axis of the 




es 


ctf 




a 


£ 


bfl 


o 


c 


^ 


a 


<L> 


>H 


c 


S3 


ctf 








s- 


C/3 


O 






M 


en 


bi) 


C 


<u 


u 


Tl 


<v 






o 




«+, 


W) 


o 


C 


<D 






o 


c 


en 





40 ELBOW PATTERNS 

semi-ellipse has here been placed parallel to the 
base line of triangle. All other operations are 
the same as in the previous example, since in 
each, it has been presumed that an elbow was to 
to be made in six pieces, at an angle of 90 
degrees. 

Had any other condition been specified, i.e., 
a change of. angle or of the number of pieces, it 
would have been met in the same general manner 
as has been discussed in Parts I and II. 

It is a difficult matter to foretell in what form 
of pipe the sheet metal worker may be called 
upon to secure the elbow patterns for. How- 
ever, since all such operations are governed by 
the same rules, the writer has for an example, 
selected a form of pipe as illustrated at Fig. 22, 
which is somewhat unusual, but by no means im- 
practicable in so far as the elbows are concerned. 
Illustrations for elbows in this form of pipe 
follow, and it is confidently hoped that upon 
giving them serious attention, the reader will 
be enabled to secure the patterns for elbows in 
any form of pipe which may come before him. 

It will be noted upon turning attention to 
Fig. 22, that in a form of pipe as here illustrated, 
i.e., one in which its cross-section is a quadrantal 



IN ANY FORM OF PIPE 



41 



triangle, the question of which way the elbow 
is to turn becomes an important one. Two sides 
of this pipe, as at a and b, are flat surfaces, and 
since a geometrical plane is defined as any flat 




Fig. 22. — Illustrating a form of pipe, the cross-section of 
which is a quadrantal triangle. 



surface, those sides, for convenience, will be 
designated as planes. Fig. 23, shows a diagram 
which may be looked upon as a cross-section, 
or a plan of a piece of pipe of this form, and the 
lines a b and a c as the plans of planes. 



42 



ELBOW PATTERNS 



We may introduce any number of right lines 
upon Fig. 23, as a d, or e f, and presume those 
lines to be the plans of additional planes, thus 
enabling us to locate a plane from its plan, 




Fig. 23. — Showing cross-section, or plan of pipe. 

parallel to which the elbow is to turn. With 
this determined, we have the key to the necessary 
position of the diagram representing the form 
of pipe, as regards the base of triangle from 
which the true lengths of lines are secured. In 
the following demonstrations will be found three 
examples of obtaining the patterns for elbows 
in a form of pipe as shown at Fig. 23, to be 
made in three pieces, and at an angle of 90 



IN ANY FORM OF PIPE 



43 



degrees. The variation is in the way the elbow 
is to turn. Figs. 24 and 25 illustrate the method 




Fig. 24. — Illustrating method of securing the true lengths of 

lines. 



of securing the lengths of lines, and transferring 
same to the material from which the elbow is 
to be made, when it is required to turn the pipe 



44 



ELBOW PATTERNS 









i 








a 

"C 

+j 

a 

M 

d 

cr 

tn 

PS 

o 








•+-> 






o 






<u 






</> 






Cfl 




N 


O 

- u 

u 






CO 


O 


K \ * 


// 5 




x \ x U tf 






w \ w / w 




a 


H \ H # — H — 


xo 


*8« 


H \ H ■ / H 




d 


< \V ^ < 




.S 


cu u /( °* 




;> 




^* 


o 
13 






CO 


a 






c3 


1 \ / 


1 




M 

O 


1 \ ' 


f 




«JH 










en 










CM ' 


s 










<u 










-M 










-*-> 










GJ 










Q* 










bo 










PJ 










• rH 










£ 










o 










^ 










C/3 
1 




















<N 










o 










M 










r^ 






Y 



IN ANY FORM OF PIPE 45 

parallel to the plane of one of its sides, or that 
side represented in plan by line a c, Fig. 23. 

Upon examination of Fig. 24, it will be noted 
that the side of the diagram representing the 
form of pipe, designated as a c, Fig. 23, has been 
placed parallel to the base line of triangle, Fig. 24. 

Since the method of obtaining the necessary 
inclination of section line has been discussed to 
some length, and, as has been previously stated, 
the inclination is dependent solely upon the 
required angle, together with the number of 
pieces, it would seem that further discussion 
upon that point would be needless repetition. 

It will be noted that the curved portion of the 
diagram representing the form of pipe, has been 
divided into a number of equal parts as 2 3 4 5, 
etc., Fig. 24, and that the vertice of the angle as 
at 1, has also been given a number. From these 
numbered points lines have been drawn, per- 
pendicular to the base line of triangle, thereby 
securing true lengths of lines to be transferred 
in the usual manner. 

Upon turning attention to Fig. 25, the reader 
will note that the line 1 1, has been drawn at 
a convenient distance from one edge of the piece 
of material from which the elbow is to be made, 



46 ELBOW PATTERNS 

and points located upon that line at the same 
relative distance from each other as found upon 
the diagram representing the form of pipe Fig. 
24. From points 1234, etc., Fig. 25, perpendic- 
ular lines are drawn as shown, upon which 
lengths are set off as found in Fig. 24, thereby 
locating points through which the irregular line 
is traced to complete one piece of the required 
pattern, when said line may be duplicated as 
shown, for the whole. 

A position of the diagram representing the 
form of pipe as shown in Fig. 24, places the heel 
at point 2. Had it been required to place the 
heel upon side 1 8, that diagram would have been 
.reversed thereby placing point 1 in the position 
now occupied by point 2. Similar principles will 
also apply to the following example. 

Fig. 26 shows the necessary diagrams when it 
is required to turn this pipe parallel to a plane 
whose position is indicated by the line a d, Fig. 
23. Fig. 2J, shows the patterns for the elbow to 
be made in three pieces, and at an angle of 
90 degrees. 

By comparing Figs. 24 and 26, it will be noted 
that the cross-section of pipe has been so revolved 
in Fig. 26 as to place a line upon that diagram 



IN ANY FORM OF PIPE 



47 



as i 5, which corresponds with a d Fig. 23, 
parallel to the base line of triangle. This is the 




Fig. 26. — Illustrating method of securing the true lengths of 

lines. 



only change in the operation of developing the 
patterns as shown at Fig. 27. 



48 



ELBOW PATTERNS 




c3 

el 
u 

cr 



CJ 

cu 

C/3 
I 

en 

g 

CJ 

<D 
en 
o 



e> 
'a ^ 

.S • 

O 

el 



el 
}-i 
<u 
^-» 

-*— > 

bO 

'% 

o 

CO 



cs 

6 



IN ANY FORM OF PIPE 



49 



In Fig. 28, it has been presumed that the 
patterns are required to turn the pipe parallel 
to a plane whose position is indicated by line 
e f, Fig. 23. 




Fig. 28. — Illustrating method of securing the true lengths of 

lines. 



Therefore in Fig. 28, the cross-section has 
been so revolved as to place a line corresponding 
to c j, Fig. 23 parallel to base line of triangle, 
thereby securing the patterns as shown at Fig. 29. 



50 



ELBOW PATTERNS 




u 
<v 

m 
O 

j-i 

CJ 
<D 

m 
O 



o 2 



bo 

c 
o 

CO 






IN ANY FORM OF PIPE 



51 



Fig. 30, shows the necessary diagrams to 
secure the patterns for an elbow in a form of pipe 
whose cross-section resembles a six pointed star. 




Fig. 30. — Illustrating method of securing the true lengths of 

lines. 



Here, as will be noted, the vertice of each angle 
has been looked upon as the points of division, 
or the plans of lines presumed to be upon said 
pipe, and numbered in the usual manner. 



52 



ELBOW PATTERNS 



x> 




% 

o 

O 

a 
i 

.^ 



O 



bX) 

S3 

• l-H 

o 

CO 



CO 

s 



IN ANY FORM OF PIPE 53 

These numbered points are now treated pre- 
cisely as in the foregoing examples, to secure the 
patterns as shown at Fig. 31, although the lines 
become somewhat involved in Fig. 30. 

The portion of the diagram representing the 
form of pipe in Fig. 30 places the heel at points 
6 and 8. Should the reader be of an inquisitive 
turn of mind, he is advised to develop a pattern 
after revolving that diagram in a manner so as 
to place points 2 and 8 in a line parallel to the 
base line of triangle, when he will have had an 
opportunity to observe more than could be 
written in pages, since practice and the conse- 
quent observations are important factors in self 
instruction, 



PART IV 

PATTERNS FOR RIVETED ELBOWS TO BE 
MADE FROM HEAVY IRON 

When the riveted elbow is demanded, the pat- 
tern cutter encounters a problem which calls for 
considerable accuracy. The rivet holes should be 
punched in the material while flat, and in proper 
positions to coincide when the elbow is assem- 
bled, thus it becomes necessary to consider the 
thickness of the material. 

If an elbow is to be made from No. 20 iron or 
lighter, the difference between the inside and 
outside diameters is negligible. On the other 
hand, as the thickness of the material increases, 
the difference between these diameters increases. 
When the material is No. 10 iron, that difference 
is approximately J4 inch. As an example, we 
may presume that a round collar is girded with 
a steel tape and found to be 113 inches. We 
note from the circumference table, page 78, that 
the diameter is very close to 36 inches. Some 

54 



ELBOWS OF HEAVY IRON 55 

error exists here since our tape which surrounds 
the collar is a circle whose diameter is one thick- 
ness of the tape more than the collar proper. 

We may cut a strip of No. 10 iron for the pur- 
pose of making a collar, and make that strip 113 
inches in length from center to center of rivet 
holes. From the circumference table on page 78, 
we have noted that the diameter of a 36 inch 
circle is approximately 113 inches, therefore we 
would in a crude way expect our collar to come 
to a 36 inch circle. However, if we measure 
this, we find an outside diameter of 36^ inches, 
and an inside diameter of 35% inches approxi- 
mately. From the above it will be noted that 
there must be allowances made for inside and 
outside diameters when using heavy materials. 

Allowances which Should be Made. 
When each joint of pipe (round, elliptical or 
oblong) is made with a large and small end, an 
allowance of from six to seven thicknesses of the 
material is required, regardless of the size. For 
example, upon referring to the table, page 85, 
we note that No. 10 iron is 9/64 of an inch in 
thickness, thereby requiring an allowance of 
from 54 to 63/64 of an inch. 



56 ELBOW PATTERNS 

If we return to the collar spoken of above, and 
presume that an inside diameter is required, we 
would multiply one thickness of the material by 
3.14, and add this product to the 113 inches. 
Thus, a collar with an inside diameter of 36 
inches made from No. 10 iron should be cut ap- 
proximately 113 7/16 inches from center to cen- 
ter of holes. Had an outside diameter been re- 
quired, we would have deducted 7/16 of an inch 
from 113, thereby making the required length of 
the collar 112 9/16 inches approximately. It is 
found in practice that the iron as it comes to the 
mechanic is not always the exact thickness given 
in tables, however the thicknesses given here are 
for illustrative purposes only. 

Having explained the necessary allowances to 
be made when working heavy material into pipe 
and elbows, we should also consider the method 
of making slips. From the lighter materials up 
to, and including No. 10, we may perhaps make 
our pipe and elbows with a large and small end, 






Fig. 32. — Illustrating the connection of joints which have 
a large and small end. 



ELBOWS OF HEAVY IRON 



57 



as illustrated at Fig. 32. In some instances, it 
may be desirable to make alternate joints equal 
in diameters to the large and small ends as shown 
at Fig. 33. This method becomes more desirable 



. r 

1 
1 

1 
L 




, — , 

1 
1 
1 
1 









Fig. 33. — Illustrating the connection of joints when made 
in two diameters. 



as the thickness of the material increases. For 
example, with No. 18 iron ^ of an inch is very 
nearly correct for a slip, thus the distortion of 
the cylindrical form is slight. On the other hand, 
should the material be Y\ inch thick, then the 
taper would be very close 1^4 inches. This is 
prohibitive, since so much taper would distort 
what should be a cylindrical form to an extent 
which can not be ignored. Each joint would then 
become in reality the frustum of a cone. There- 
fore with the heavier materials, it would seem 
better to follow the example of the boiler maker 
and make our joints of constant diameters and 
of two sizes. 



58 ELBOW PATTERNS 

Spacing for Rivet Holes where Joints are to be 

Connected. 
As illustrated at Fig. 34, rivets which pass 
through the ends of the joints where connected 




Fig. 34. — Showing the relative position of rivet holes in 

the large and small ends of joints where 

connected 

may be conceived as being in radial lines from 
the center. Therefore each circumference is us- 
ually divided into the same number of equal 
parts. For example, we may presume to have a 
joint of 36 inch pipe to be made from No. 10 
iron. As has been explained, this gives us two 



ELBOWS OF HEAVY IRON 



59 



lengths to be divided, i.e., the circumferences of 
the large and small ends, the variation of which 
is, in this instance approximately % of an inch. 
It is usually desirable to have the number of 
connecting holes divisible by four, therefore we 
divide those lengths into four parts, then subdi- 
vide each part to suit the desired number of rivets 
in the connection. 

It should be remembered that the variation in 
the sizes which the large and small ends should 
be made is wholly dependent upon the thickness 
of the material used for round, elliptical or ob- 
long pipe, regardless of size. Rivet holes at the 
ends of joints where connected are spaced pro- 
portionately in round or elliptical pipe. In ob- 
long pipe, a section of which is shown at Fig. 





Fig. 35. — Showing the relative position of rivet holes in 
the large and small ends of joints in oblong pipe. 



60 ELBOW PATTERNS 

35, the curved portions are spaced proportion- 
ately, with the straight sides spaced equally as 
will be noted upon examination of Fig. 35. 

To Develop the Patterns. 

The development of the patterns for the riv- 
eted elbow to be made from heavy material dif- 
fers in no essential respect from methods shown 
in the earlier pages of this work. On the other 
hand, some modifications can be made to suit ex- 
isting conditions. This explanation will be de- 
voted to securing the patterns for a square elbow 
in 36 inch round pipe, to be made m five pieces, 
from No. 10 iron. Since changes in the gauges of 
material, the sizes of pipe, or the angle of the 
elbow simply changes dimensions, not the prin- 
ciples involved, the student should have little 
difficulty in applying those methods to elbows 
of various sizes, angles, number of pieces and 
gauges of material. 

Presuming, as stated above, that a 36 inch el- 
bow in round pipe is required, to be made from 
No. 10 iron, in five pieces and with a specified 
radius of throat of 18 inches, we may proceed 
somewhat as follows : In any convenient posi- 
tion draw an indefinite right line as A B, Fig. 36. 



ELBOWS OF HEAVY IRON 



61 




Fig. 36. — Diagrams necessary to secure the true length 
of lines to be transferred to the pattern. 



From some point along this line as at C, draw a 
semi-circle to represent a semi-plan of the 36 inch 
round pipe, as 1 6 11 as shown. 

It may be here explained that if a 36 inch 
inside diameter is required, this semi-circle 
should be increased one thickness of the iron 



62 ELBOW PATTERNS 

above the required diameter, i.e., it should be 
made 36^ inches. From point D along the line 
D B set off a distance equal to the required ra- 
dius of the elbow at the throat as at B. With 
point B as center and D B as radius, describe an 
arc as shown. With trummels set to a radius 
equal to the distance from B to 1, and with point 
B as center, describe the large arc as also shown. 
From point B draw a line as B E perpendicular 
to line A B. Divide the arc 1 E into two equal 
parts as at F. Since the elbow is to be made in 
five pieces, we divide the arc 1 F into four equal 
parts as at G H and /. Upon drawing the line 
G B we have the inclination of the miter cut 
for all sections of the elbow. 

Since we may best locate our rivet holes along 
elements of the cylindrical form it may be well 
to determine the number required in each mi- 
tered seam, then divide the semi-circle repre- 
senting the cylinder into a number of parts which 
is divisible without remainder by the number of 
rivets required. For example, should 8 or 16 
rivets be required, we may divide the semi-circle 
into 8 parts, should 10 or 20 rivets be required 
we could then divide the semi-circle into 10 parts, 



ELBOWS OF HEAVY IRON 



63 



and so on for any required number. It is pre- 
sumed in this example that 20 rivets are re- 
quired in each mitered seam, and the same num- 
ber at the ends of the elbow where it is to be 
connected to the straight pipe, therefore points 
upon the semi-circle are located as shown. Lines 
drawn through those points of division perpen- 
dicular to A B as shown, then supply all neces- 
sary measurements for locating points upon the 
curved line of the pattern. 

Since accuracy and simplicity are elements 
which should be considered, the author recom- 
mends that a pattern for one-half of one end 
section including the necessary rivet holes, as 
shown at Fig. 37 be cut from some light mate- 



/ 


2 


3 


4 


6 


6 


7 








8 


9 tO 


// 




1 


i._ 1 


1 


1 


> • 


1 


- 


1 


» . 1 



Fig. 37. — A Pattern cut from light material. 



rial. Here as will be noted, lengths of lines sup- 
plied at Fig. 36, are transferred to similarly 
designated lines of the pattern. Rivet holes are 



64 



ELBOW PATTERNS 






<L> 



o 



J-l 

o 

a 

u 

<l> 
H 



oo 

CO 

d 



ELBOWS OF HEAVY IRON 65 

considered as points in the curved line of the pat- 
tern, and the necessary lap added. This lap 
cannot be too small, on the other hand it should 
not be too large as an increased width adds to 
the difficulty of assembling the elbow. A margin 
of one-half inch from center of rivet holes usu- 
ally gives very satisfactory results. 

Presuming that a pattern as shown at Fig. 37 
has been cut from light material, we may test 
its accuracy by placing it upon a flat surface and 
marking the curved line and holes. Upon re- 
versing it, the curved line and holes should coin- 
cide in their order. Finding our pattern correct, 
we now proceed to reverse and revolve it upon 
the material from which the elbow is to be made, 
to secure results as shown in a reduced scale 
at Fig. 38. This process is substantially the same 
as was explained in Part 2. 

Distortion Caused by Taper at the Small End. 
A constant diameter of the elbow is main- 
tained except at the small end shown at Fig. 
38. Here as will be noted, the circumference 
has been decreased the necessary amount for a 
slip, and rivet holes placed accordingly. This 
causes some distortion, however, if we can se- 



66 ELBOW PATTERNS 

cure a length of 8 inches or more, this may be 
ignored. Two longitudinal seams in this sec- 
tion will, with a portion of the taper in each, 
still further reduce the distortion. 

In some instances, one is called upon fdr an 
elbow with a relatively short small end, in which 
case, providing the elbow must be assembled with 
the laps all one way, a somewhat serious prob- 
lem is encountered. The required taper forces 
this section into a far from normal condition. 
To overcome this, we may employ slightly dif- 
ferent methods which are hereinafter explained. 

The student's attention is directed to the fact 
that GAD, Fig. 36, can be conceived as being 
an elevation of a portion of the elbow at its ex- 
tremities, also one-half of each intermediate sec- 
tion of which there are three in this example. 
Any length added below the line A D is simply 
an added length of pipe, and has no direct in- 
fluence upon the elbow. On the other hand, this 
length must be preserved as one-half of each 
intermediate section to maintain the specified ra- 
dius of throat. A change in the length of the 
intermediate sections will not change the angle, 
however it will change the distance in which 



ELBOWS OF HEAVY IRON 67 

the elbow turns. Some attention to the earlier 
pages of this work, and an examination of Figs. 
36, 37 and 38 should give the student a clear 
understanding of the problem now before us. 

A Substitute Method. 

The author's attention has many times been 
called to a substitute method wherein taper is 
introduced into each section. While this method 
proves quite satisfactory, it distorts the whole 
elbow to some extent, and the sections must be 
assembled in the same order as cut from the ma- 
terial. Some mention will be made of it, and 
allow the operator to judge for himself. In 
examples where unusually short small ends are 
called for, some advantage may be gained, as 
the difference in circumference between any two 
connecting sections is then slight. 

When diagrams are drawn for the purpose of 
determining the lengths of lines to be transferred 
to the pattern, those diagrams are usually made 
upon the presumption that the elbow has a con- 
stant diameter. When we taper the elbow our 
diagrams are then somewhat in error. However 
when confronted with two evils, we may consist- 
ently choose the least. 



68 



ELBOW PATTERNS 



1 
















r -f- - 


















T 




r ~^~~- 


» 






























\ 




1 

! 1 

"i 

— -i 


/ 


















i 
- — -i 

1 

1 

1 

r\ 




















1 

I 


1 


















1 

i 
i 




















- <H 


c 


















ffl 


Z .. TT 


















1 
" ~1 



Fig. 39. — The semi-pattern for an elbow to be riveted. 

Fig. 39 shows the semi-pattern for substan- 
tially the same elbow as previously explained. 
Here, as will be noted, the large and small ends 



ELBOWS OF HEAVY IRON 69 

have been established upon a suitable portion 
of the material, and rivet holes located at each 
of these ends. Lines are then drawn between 
corresponding rivet holes previously located at 
the large and small ends as shown, which com- 
pare in a measure with the usual equidistant 
parallel lines. At a suitable distance from the 
small end, a line is drawn which may be pre- 
sumed to be the line I n, Fig. 36. Points in the 
curved line, or the rivet-holes are located in pre- 
cisely the same manner as has been previously 
explained. 

Having developed the pattern as shown at 
A B C D Fig. 39, which is in this instance, the 
small end of the elbow, we must now develop 
the patterns for the remaining sections. To ac- 
complish this we locate lines as X Y Fig. 39 at 
the required distance from C D to allow the set- 
ting off of distances above and below those lines 
as was set off above C D. 

Some study of the construction lines shown 
in Fig. 39, and a comparison of measurements 
found in that diagram with those found in Fig. 
36, should enable the student to complete his pat- 
tern as shown. We must locate each point or 



70 ELBOW PATTERNS 

rivet hole, since no two are at the same distance 
from each other. Here, far more spacing is called 
for with a consequent loas of accuracy, however, 
satisfactory results are often secured. 

Assembling the Elbow. 
When the pattern is developed as above ex- 
plained, the elbow is usually assembled with laps 
all one way, as from left to right, Fig. 32. The 
ends of the sections which go inside are drawn 
in at the heel somewhat more than the angle 
at which the sections meet, and gradually re- 
duced to the center of the throat. The ends of 
the sections which go outside are drawn out at 
the throat slightly more than the angle at which 
the sections join, and gradually diminished to 
the center of the heel. To preserve the relative 
distance between the rivet holes we should draw 
one section in the same amount as we draw out 
the other. Since our sections where connected 
are normally the same circumference, one must 
be drawn in to average one-half the thickness 
of the material, while the other is' drawn out a 
similar amount. Should the connections be some- 
what overdrawn, the rivets will draw them into 
position, when the edges may be dressed up. 



ELBOWS OF HEAVY IRON 71 

Considerable difference in appearance is noted 
in elbows assembled by different mechanics. 
Some skill is demanded, and with this very pleas- 
ing results are obtained. 

Elbows in Extremely Heavy Material. 
When the material is thicker than No. 10, no 
doubt — more satisfactory results will be obtained 
by making the sections of two diameters, the 
variation being sufficient for one to pass inside 
the other, or that variation necessary for a large 
and small end. We may then develop our pat- 
terns as shown at Figs. 36 and 37 for each size. 
We should then draw the semi-circles to repre- 
sent each size in separate positions, and divide 
each into the same number of parts, then proceed 
with each size as with an elbow whose sections 
are of one diameter. It should be remembered 
that if we begin with a section of small diameter, 
the next should be a large one, and so on for the 
full number. Each large section acts as a sleeve 
to connect the small ones each side of it. In 
this way no drawing is required at the ends of 
the sections except to change the direction where 
those sections lap. 



72 ELBOW PATTERNS 

Spacing for Rivet Holes. 
A very simple appliance for spacing rivet holes 
is shown at Fig. 40. Rivets in long seams are 
usually spaced at a constant distance, i.e., at a 
specified distance from center to center. This 
distance is sometimes known as the pitch of the 
rivets. 

ppr\r\r\iArATNr\r^^ 

Fig. 40. — An appliance for locating rivet holes. 

The appliance shown at Fig. 40 is simply a 
strip of light material in which notches have 
been cut at a constant distance from each other 
to suit the required pitch of rivets. If this notch- 
ing has been accurately done, we have a gauge 
from which rivets may be located along a straight 
line with far more accuracy than by the use of 
compasses, 



APPENDIX 

THE CIRCLE 

A Circle is a plane figure bounded by a curve, 
all points of which are equally distant from a 
point within called the Center. The Circle 
includes a greater area than any other form of 
equal perimeter, i.e., equal length of outline. 

The curve which bounds the circle is called the 
Circumference, and any portion of it is called 
an Arc. 

A Chord is a straight line which joins any two 
points on the circumference, as a b y or c d, 
Fig. 32. 

When a chord passes through the center as 
c e d, Fig. 32, it has its greatest length, and is 
called the Diameter. 

A Radius is the length of a straight line 
drawn from the center to the circumference, as 
c e or c d, Fig. 32, and is equal to one-half the 
diameter. 

There is a constant ratio between the circum- 
ference of a circle and its diameter : the value of 

73 



74 ELBOW PATTERNS 

this ratio to six figures is 3. 141 59. For most 
purposes it is sufficient to take 3.1416, and in 
many cases 3.14, or approximately 2 T 2 -, which 
is a convenient vulgar fraction, the error being 
about one part in two thousand. 




Fig. 32. 

To find the circumference of a circle, multiply 
its diameter by 3.14, or if vulgar fractions are 
preferred, multiply the diameter by %&. The 
table here appended will obviate those calcula- 
tions many times. 



APPENDIX 



75 



To secure the approximate circumference of 
a circle by a graphical method 

Describe a circle of the required diameter as 
shown at Fig. 33. By the use of the steel square, 




Fig. 33. 

draw radial lines from the center of circle at 
right angles to each other as b a, and a c. From 
the intersections of said lines with the circle as 
at b and c, draw the line b c. From the center of 



76 



ELBOW PATTERNS 



line b c, as at d, draw the perpendicular line d e. 
Multiplying the diameter of circle by three, and 
adding the length of line e d, will determine the 
circumference close enough for all practical 
purposes, or perhaps within six one-hundredths 
of an inch for a 12 inch circle. The area of 
circles are to each other as the square of their 
diameter, thus the area of a 20 inch circle is 
equal to four 10 inch. 

To find the area of a circle, multipy the 
square of its diameter by .7854. 

Areas and Circumferences of Circles 

To find the circumference of a circle whose 
diameter involves the smaller fractions of an 
inch, take the circumference as found for the 
full number of inches, and add the circumference 
of the fraction as given. For example, let it be 
presumed that the circumference of a 22$/% inch 
circle is required. 

We find from the table, the circumference of 
a 22 inch circle to be 69.1152, and the circum- 
ference of a Y% inch to be 1.9635, which we add 
to 69.1152 thus finding the circumference of a 
22^ inch circle to be 71.0787 inches. 



APPENDIX 



77 



Diam. 


Circum. 


Area. 


Diam. 


Circum. 


Area. 


A 


.0491 


.0002 


•A 


23.5620 


44.1787 


A 


.0982 


.0008 


8 


25.1328 


50.2656 


A 


.1963 


.0031 


81 


26.7036 


56.7451 


1 
8 


.3927 


.0123 


9 


28.2744 


63.6174 


ft 


.5890 


.0276 


9i 


29.8452 


70.8823 


l 

4 


.7854 


.0491 


10 


31.4160 


78.540 


A 


.9817 


.0767 


10 J 


32.9868 


86 . 590 


3 
8 


1.1781 


.1104 


II 


34-5576 


95.033 


A 


1-3744 


.1503 


II* 


36.1284 


103 . 869 


J 


1.5708 


.1963 


12 


37.6992 


113.098 


A 


1 .7671 


.2485 


12* 


39.2700 


122.719 


f 


I-9635 


.3068 


13 


40 . 8408 


132.733 


fi 


2.1598 


.3712 


13* 


42.4116 


143-139 


3 
4 


2.3562 


.4418 


14 


43.9824 


153 938 


u 


2-5525 


.5185 


14* 


45-5532 


165.130 


1 

8 


2 • 7489 § 


.6013 


15 


47.1240 


176.715 


« 


2.9452 


.6903 


IS* 


48 . 6948 


188.692 


I 


3.1416 


.7854 


16 


50.2656 


201.062 


ii 


4.7124 


I. 7671 


16* 


51.8364 


213.825 


2 


6.2832 


3.1416 


17 


53.4027 


226.981 


2| 


7-8540 


4.9087 


17* 


54.9780 


240.529 


3 


9.4248 


7.0686 


18 


56.5488 


254.470 


3* 


10.9956 


9.6211 


18J 


58.1196 


268.803 


4 


12.5664 


12.5664 


19 


59 • 6904 


283.529 


4} 


14.1372 


IS-9043 


19* 


61 .2612 


298.648 


5 


15.7080 


19.6350 


20 


62.8320 


314.160 


5* 


17.2788 


23 • 7583 


20J 


64.4028 


330.064 


6 


18.8496 


28.2744 


21 


65-9736 


346.361 


6* 


20.4204 


33-I83I 


21* 


67-5444 


363.051 


7 


21 .9912 


38.4846 


22 


69.1152 


380.134 



78 



ELBOW PATTERNS 



Diam. 


Circum. 


Area. 


Diam. 


Circum. 


Area. 


22* 


70.6860 


397.609 


37* 


117. 8lO 


1104.469 


23 


72.2568 


415.477 


38 


119. 381 


1134.118 


23i 


73.8276 


433-737 


38i 


120.925 


.1164.159 


24 


75-3984 


452.390 


39 


122.512 


•H94-S93 


24* 


76.9692 


471.436 


39* 


124.093 


• 1225.420 


25 


78 . 5400 


490.875 


40 


125.664 


• 1256.640 


25* 


80.II08 


510.706 


40* 


• 127.235 


■ 1288.250 


26 


81.6816 


530 .930 


41 


128.806 


1320.260 


26* 


83-2524 


551-547 


4*2 


130.376 


1352.660 


27 


84.8232 


572.557 


42 


131-947 


1385. 45o n 


2 7 * 


86 . 3940 


593-959 


42* 


I33-5I8 


1418.630 


28 


87.9648 


6i5-754 


43 


135 089 


1452.200 


28* 


89-5356 


637.941 


43* 


136.660 


i486. 170 


29 


91 .1064 


660.521 


44 


138.230 


1520.53 


29* 


92.6772 


683.494 


44* 


139.801 


I555-29 


30 


94. 2480 


706.860 


45 


141.372 


1590.43 


30* 


95.8188 


730.618 


45* 


142.943 


1625.97 


3i 


97.3896 


754-769 


46 


144.514 


1661 .91 


31* 


98.9604 


779.313 


46i 


146.084 


1698.23 


32 


100.5312 


804.250 


47 


I47-655 


1734-95 


32* 


102. 1020 


. 829.579 


47 1 


149.226 


1772.06 


33 


103.673 


855-3oi 


48 


150.797 


1809.56 


33i 


105.244 


881.415 


48* 


152.368 


1847.46 


34 


106.814 


907.922 


49 


*53 -938 


1885.75 


34* 


108.385 


934.822 


49* 


I55-509 


1924.43 


35 


109.956 


962.115 


50 


157.080 


1963.50 


35i 


in. 527 


989 . 800 


5o! 


158.651 


2002.97 


36 


113.098 


1017.878 


5i 


160.222 


2042.83 


36i 


114.668 


1046.349 


5ii 


161.729 


2038.08 


37 


116.239 


1075.213 


52 


163.363 


2123.72 



APPENDIX 



79 



Diam. 


Circum. 


Area. 


Diam. 


Circum. 


Area. 


5*1 


164.934 


2164.76 


62! 


196.350 


3067.97 


53 


166.505 


2206.19 


63 


197.921 


3117.25 


S3* 


168.076 


2248.OI 


63! 


119.492 


3166.93 


54 


169.646 


2290. 23 


64 


201 .062 


3 2 1 7 . 00 


54i 


171 .217 


233 2 -83 


Hh 


202.633 


3267.46 


55 


172.788 


2375-83 


65 


204 . 204 


33*8-3* 


SSi 


174-359 


2419.23 


65i 


205.775 


3369 -56 


56 


I75-930 


2463 .01 


66 


207.346 


3421 . 20 


56i 


177.500 


2507.19 


66J 


208.916 


3473 • 24 


57 


179.071 


255I-76 


6 7 


210.487 


3525-66 


57i 


180.642 


2596.73 


67i 


212.058 


3578.48 


58 


182.213 


2642.09 


68 


213.629 


3631.69 


58i 


183.784 


2687.84 


68J 


215.200 


3685.29 


59 


185.354 


2733-98 


69 


216.770 


3739-29 


59* 


186.925 


2780.51 


6 9 i 


218.341 


3793-68 


60 


188.496 


2827.44 


70 


219.912 


3848.46 


60^ 


190.067 


2874.76 


70J 


221.483 


3903 • 63 


61 


191.638 


2922.47 


7i 


223.054 


3959- 20 


61J 


193. 208 


2970.58 


n\ 


224.624 


4015.16 


62 


194.779 


3019.08 


72 


226.195 


407I-5I 



The Ellipse 

The Ellipse is a curve in which the sum of 
the distances of each point from two fixed points 
called the Foci, is equal to a given line. 

The straight line drawn through the foci and 



80 



ELBOW PATTERNS 



terminated by the curve as at A B, Fig. 34, is 
called the Major, or Transverse axis, and the 
middle of that line as at E, is the Center of the 
ellipse. 




Fig. 34. — Illustrating a method of describing an ellipse. 



The straight line drawn through the center 
at right angles to the major axis, and terminated 
b}' the curve as at C D, is called the Minor or 
Conjugate axis. 



APPENDIX 81 

To draw an ellipse in given dimensions 

Draw the two diameters as A B, and C D, 
Fig. 34 at right angles to each other intersecting 
at their centers as at E. With point E as center, 
describe two circles, one with radius E A, and 
one with radius E C, as shown. Divide each 
quarter of the large circle into the same number 
of equal parts as at I 2 3 4, etc., and draw lines 
from center E to intersect these points, thus 
dividing the small circle into the same number 
of equal parts as at a b c d e and /. Connect 
similar numbered points upon the large circle 
with vertical lines, and through the similar 
lettered points upon the small circle draw 
horizontal lines. The intersections of said lines 
as at x y z, are points in an ellipse whose 
dimensions have been specified in lines A B and 
CD. 

To drazv an approximate ellipse 

Draw the two diameters A B, and C D. Fig. 35, 
at right angles to each other, and intersecting at 
their centers as at E. Locate point a at a distance 
from A equal to C D, and divide line a B into 



82 



ELBOW PATTERNS 



three equal parts as at I 2 3. Locate points b b 
at a distance from E equal to a 2. From points 
b b as centers, with compasses set to a distance 
equal to b b, describe arcs intersecting each other 




Fig. 35 — Illustrating the method of describing an approxi- 
mate ellipse. 



as at point c c. From points c c draw right 
lines through points b b. From points c c as 
centers, and C C or c D as radius, describe arcs 
intersecting lines c b produced. From points b, 
with b A or b B as radius, draw arcs meeting 



APPENDIX 



83 



those previously drawn, which completes the 
figure as shown. 

This is sometimes called a false ellipse, since 
strictly speaking, no part of an elliptical curve 
is a part of a circle, however, this figure closely 
approximates the ellipse, and is to be preferred 
in some cases. 

To determine the circumference of an ellipse 

Multiply the sum of the semi-major and 
semi-minor axes by 3.1416. As for example, 
find the circumference of an elipse whose 
diameters are 8 and 12 inches. The solution 
arrived at would be as follows: 4+6X3.1416= 
31.416. 

To find the area of an ellipse, multiply the 
length of the major axis by the length of the 
minor axis, and this product by .7854. 

The Protractor 

The Protractor is an instrument for measur- 
ing, or laying off angles, consisting usually of a 
graduated arc, or circle. The protractor as found 
in the cheaper grades is commonly divided to 



84 



ELBOW PATTERNS 



one degree, although in some instances it is found 
divided to one-half degree. 




Protractor. 



The more expensive grades have a vernier 
which reads to five minutes, or one-twelfth of 
a degree. 



APPENDIX 



85 



UNITED STATES STANDARD GAUGE AND WEIGHTS 
OF SHEET STEEL 

As given by the manufacturer 



Number 

of 
Gauge. 


Approximate 

Thickness in 

Fractions of 

an Inch. 


Approximate 
Thickness in 

Decimal 

Parts of an 

Inch. 


Weight per 
Square Foot 

in Ounces 
Avoirdupois. 


Weight per 
Square Foot 

in Pounds 
Avoirdupois. 


ooooooo 


1/2 


•5 


320 


20.00 


oooooo 


15/32 


.46875 


300 


18.75 


ooooo 


7/l6 


•4375 


280 


I7.50 


oooo 


1 3/S2 


.40625 


260 


16.25 


ooo 


3/& 


•375 


240 


15 


oo 


11/32 


•34375 


220 


13-75 


o 


5/i6 


•3125 


200 


12.50 


I 


9/32 


.28125 


180 


11.25 


2 


17/64 


.265625 


170 


10.625 


3 


1/4 


•25 


160 


10 


4 


15/64 


•234375 


I50 


9-375 


5 


7/32 


.21875 


140 


8-75 


6 


13/64 


.203125 


130 


8.125 


7 


3/i6 


.1875 


I20 


7-5 


8 


11/64 


.171875 


no 


6.875 


9 


5/32 


•15625 


IOO 


6.25 


IO 


9/64 


.140625 


90 


5-625 


ii 


1/8 


•125 


80 


5 


12 


7/64 


•109375 


70 


4-375 


13 


3/32 


•09375 


60 


3-75 


14 


5/64 


.078125 


50 


3-125 



86 



ELBOW PATTERNS 



UNITED STATES STANDARD GAUGE AND WEIGHTS 
OF SHEET STEEL— Continued 



Number 

of 
Gauge. 


Approximate 

Thickness in 

Fractions of 

an Inch. 


Approximate 
Thickness in 

Decimal 

Parts of an 

Inch. 


Weight per 
Square Foot 

in Ounces 
Avoirdupois. 


Weight per 
Square Foot 

in Pounds 
Avoirdupois. 


15 


9/128 


.0703125 


45 


2.8125 


16 


1/16 


.0625 


40 


2-5 


17 


9/160 


.05625 


36 


2.25 


18 


1/20 


.05 


32 


2 


IQ 


7/160 


.04375 


28 


1-75 


20 


3/8o 


•0375 


24 


I-50 


21 


n/320 


.034375 


22 


1-375 


22 


l/32 


.03125 


20 


1.25 


23 


9/320 


.028125 


18 


1. 125 


24 


1/40 


.025 


16 


1 


25 


7/320 


.021875 


14 


.875 


26 


3/160 


.01875 


12 


•75 


27 


n/940 


.OI7I875 


11 


.6875 


28 


1/64 


.015625 


10 


.625 


29 


9/640 


.0140625 


9 


•5625 


30 


1/80 


.0125 


8 


•5 


31 


7/640 


•OIO9375 


7 


•4375 


32 


13/1280 


.OIO15625 


6* 


.40625 


33 


3/320 


.009375 


6 


•375 


34 


u/1280 


.00859375 


si 


•34375 


35 


5/640 


.0078125 


5 


•3125 


36 


9/1280 


.00703125 


4* 


.28125 


37 


17/2560 


.006640625 


4 


.265625 


38 


1/160 


.00625 


4 


.25 



APPENDIX 



87 



WEIGHT PER SQUARE FOOT OF GALVANIZED 

SHEETS 





As 


given by the manufacturer 




Number. 


Pounds. 


Number. 


Pounds. 


Number. 


'Pounds. 


12 


4-53 


20 


1. 6 S 


27 


.843 


14 


3.28 


22 


I .40 


28 


.781 


16 


2.65 


24 


i-i5 


29 


.718 


l8 


2.15 


26 


.90 


30 


•65 



The Metric System 



Measures of length 

The metric system having been legalized by 
the United States Government, no doubt a dis- 
tinct advantage would be gained by its more 
general use. 

In all mathematical calculations involving 
length, area, or volume, decimal fractions are 
more easily computed than vulgar fractions, in 
which we become involved when using feet and 
inches. To suit convenience, either for very 
large or very small measurements other units 
have to be derived from these by taking definite 
fractions, or multiples of them. 



88 ELBOW PATTERNS 

There is no doubt that with the system 
universally in vogue, it is most convenient to 
take each smaller unit as one-tenth of the one 
above, and each larger unit as ten times the one 
below. This is done in the metric system, as 
shown by the following tables. 

THE METRIC SYSTEM 

Measures of Length 

io milli-meters i centi-meter = 0.3937 inches 

10 centi-meters 1 deci-meter = 3.937 inches 

10 deci-meters 1 meter = 39.37 inches 

10 meters 1 deca-meter = 303 . 7 inches 

10 deca-meters 1 hecto-meter= 328 feet 1 inch 

10 hecto-meters 1 kilo-meter =3280 feet 10 inches 



INDEX 

PAGE 

Adjustable Elbow, Analysis of 5-6 

Allowances which Must be Made in Heavy Iron.. 55 

Altitude of Heel, Rule to Find 9 

Altitude of Heel, Found on the Steel Square.... 12 

Analysis of the Elbow in Round Pipe 1 

Angle of the Component Elbow, To Determine 9 

Angles, Measurement of 1 

Angle, Variation of, in Making Up Elbows 23 

Appliance for Spacing Rivet Holes 72 

Areas of Circles 76 

Area of a Circle, To Determine 76 

Area of an Ellipse, To Determine 83 

Assembling the Elbow 70 

Axis of an Ellipse 80 

Changing the Length of the Intermediate Section. 66 

Circle, The 73 

Circle, To Determine the Area of... 76 

Circle, To Determine the Circumference of 74 

Circle, To Determine the Circumference of, by 

Graphical Method ,. . . 75 

Development of Pattern for Riveted Elbow 60 

Elbow in Round Pipe 9 

Elbow in Elliptical Pipe, Turning Parallel to its 

Maj or Axis 34 

Elbow in Elliptical Pipe, Turning Parallel to its 

Minor Axis „ 37 

89 



90 INDEX 

PAGE 

Elbow in Oblong Pipe, Turning Parallel to its 

Maj or Axis 26 

Elbow in Oblong Pipe, Turning Parallel to its 

Minor Axis 30 

Elbow in a Form of Pipe whose Cross-section is a 

Quadrantal Triangle. First Example 42-46 

Elbow in a Form of Pipe whose Cross-section is a 

Quadrantal Triangle. Second Example 46-48 

Elbow in a Form of Pipe whose Cross-section is a 

Quadrantal Triangle. Third Example 49~5c 

Elbow in a Form of Pipe whose Cross-section 

Resembles a Six-pointed Star 51-53 

Elbow, Riveted, of Heavy Iron , 54 

Ellipse, The 79 

Ellipse, To Determine the Area of 83 

Ellipse, To Determine the Circumference of 83 

Ellipse, To Draw an Approximate 81 

Gauges and Weights of Sheet Steel, Manufac- 
turers' Table 85-86 

Graphical Method of Determining the Circumfer- 
ence of a Circle 75 

Heavy Iron Elbows 54 

Inside and Outside Diameters 56 

Laps at the Mitered Seams ,. . . 65 

Length of Pieces in Throat 22 

Locating Rivet Holes Along the Mitered Seams. . 62 

Locating Rivet Holes in Oblong Pipe ,. 59 

Making up Elbows, Variation in 23 

Measurement of Angles 1 

Methods of Making Joints 56 



INDEX 91 

PAGE 

Metric System. 87 

Patterns for an Elbow with Seams at Throat and 

Heel 18 

Patterns for an Elbow with Seams at the Side... 20 

Protractor, The 83 

Protractor, The Use of io-n 

Reducing Distortion in the Tapered Small End... 65 

Riveted Elbow 54 

Rule to Find the Altitude of Heel 9 

Rule to Find the Angle of Component Elbow 9 

Skill Required to Assemble the Elbow 71 

Spacing for Rivet Holes 58 

Table of Circumferences and Areas 77~79 

Testing Accuracy of the Pattern 65 

Thickness of Material Considered 54 

To Designate the Way an Elbow is to Turn whose 

Diameters are not Constant 24-26 

To Determine the Angle of Component Elbow. ... 9 

To Determine the Area of a Circle j6 

To Determine the Area of an Ellipse 83 

To Determine the Circumference of a Circle 74 

To Determine the Circumference of a Circle by 

Graphical Method 75 

To Determine the Circumference of an Ellipse 83 

To Draw an Approximate Ellipse 81 

To Draw the Curved Line upon which an Elbow 

Pattern is Cut. First Method 13 

To Draw the Curved Line upon which an Elbow 

Pattern is Cut. Second Method 16 

To Draw an Ellipse 80 



92 INDEX 

PAGE 
Use of the Steel Square in Finding the Altitude 

of Heel 12 

Variation of Angle in Making up Elbows 23 

Weights of Galvanized Iron per Square Foot, ■ 

Manufacturers' Table 69 

When the Small End is Unusually Short 66 



